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Finding the Fourth Proportional to 428.42, 642.12 and 209

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Solution

The fourth proportional to 428.42, 642.12 and 209 is: 313.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    428.42 : 642.12 = 209 : x
  2. Step 2: Convert to fraction form
    428.42/642.12 = 209/x
  3. Step 3: Cross multiply
    428.42x = 642.12 × 209
  4. Step 4: Simplify right side
    428.42x = 134,203.08
  5. Step 5: Solve for x
    x = 134,203.08/428.42
  6. Step 6: Final answer
    x = 313.25

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.